One of the most important feature of federalism, in retrospect, is that it makes the government more robust in the face of events like the current federal government shutdown due to Congressional gridlock.
A great many functions of government are carried out and funded by state and local governments that are not subject to the shutdown. My children's public schools are open. Police are out enforcing the laws at the traffic corner. It is business as usual for firefighters. Municipal water and sewer systems are still operating. The buses and light rail are running. The construction of new light rail lines continues unabated. State courts which handle the bulk of the civil and criminal dockets are open force business, and the business transactions managed by the Colorado Secretary of State are not impeded.
While the postal service is part of the federal government, because it is a largely user's fee funded independent agency, the mail is still being delivered. Similarly, the Federal Reserve System, which is quasi-private is still running.
This isn't to say that there isn't an effect. I have a client's federal tax audit on hold. The federal courts in which I have appearances entered in several cases believe that they will run out of money in about ten days. The 8th graders at Hamilton Middle School are likely to have their class trip to Washington D.C. set for two weeks from now, spoiled. Federal parks and museums are closed. Medicare claims processing will grind to a near halt. New passports are not being issued. Many federal government workers with "essential" functions aren't paid and are working on faith that they will be paid retroactively when the deadlock is over.
Funded or not, the military and federal prisons can't practicably shut down on a dime because the Congress won't appropriate funds to pay for them.
Ultimately, House Republicans may have managed to snatch defeat from the jaws of victory in the 2014 election as a result of their little stunt. They've gone to the barricades to protect the right of Americans to be sick and too broke to receive healthcare at the same time, and surely must know that they are on the wrong side of history on this one. But, self-delusion is powerful magic indeed.